Longitudinal-field measurements

In Fig.30, we show $\mu$SR spectra from longitudinal field (LF) decoupling measurements, which investigate fluctuations of the internal fields (see section 3.4). The spectra in longitudinal fields clearly demonstrate the static nature of the muon relaxation, being consistent with the observation of the `1/3-component' and the `dip' in the zero-field measurements. The recoveries of the muon spin polarization in LF's are well described by the static Gaussian Kubo-Toyabe theory (solid lines in Fig. 30), which seems to imply a random freezing of moments, rather than true Néel order. However, as a local probe, the $\mu$SR results can not exclude the possibility of long range spin correlations. When there is a distribution of $T_{\rm N}$,the muon spin precession is sometimes smeared out because of the distribution in the local fields (See the discussion in Chapter 6 for an example.) Therefore, we just propose an existence of a static order at $T\sim 52$ K in the 3-leg ladder system.

  

Figure 30: Longitudinal field (LF) decoupling measurements of the 3-leg ladder system at 50 mK. The solid lines are the fit with static Kubo-Toyabe functions (eq.19).